Topological Constraints on Magnetic Relaxation

Yeates, Anthony R.; Hornig, G.; Wilmot-Smith, A. L.

doi:10.1103/physrevlett.105.085002

Cited by 64 publications

(77 citation statements)

References 21 publications

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“…Although the evolution is resistive and there is widespread reconnection as the field relaxes, the relaxation is sufficiently fast to preserve the initial helicity H r ¼ 0, as predicted by Taylor theory. 7 But contrary to Taylor theory, which would predict a uniform relaxed field B ¼ e z with A 0, the final state maintains equal regions of positive and negative A, manifesting itself in non-trivial topology of the field lines in the end-state of the relaxation, despite the conservation of helicity 15 (see also Ref. 16).…”

Section: A Field Line Helicitymentioning

confidence: 94%

Unique topological characterization of braided magnetic fields

Yeates

Hornig

2013

Physics of Plasmas

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We introduce a topological flux function to quantify the topology of magnetic braids: non-zero, line-tied magnetic fields whose field lines all connect between two boundaries. This scalar function is an ideal invariant defined on a cross-section of the magnetic field, and measures the average poloidal magnetic flux around any given field line, or the average pairwise crossing number between a given field line and all others. Moreover, its integral over the cross-section yields the relative magnetic helicity. Using the fact that the flux function is also an action in the Hamiltonian formulation of the field line equations, we prove that it uniquely characterizes the field line mapping and hence the magnetic topology. V C 2013 American Institute of Physics.

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Section: A Field Line Helicitymentioning

confidence: 94%

Unique topological characterization of braided magnetic fields

Yeates

Hornig

2013

Physics of Plasmas

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“…There is perhaps, for some field configurations, another constraint that decides the relaxed state, such as the topological degree of the field line mapping between the ends of the loop, as investigated by Yeates et al (2010). They examined two braided magnetic field configurations (one based on the simple pigtail braid and the other more complex).…”

Section: Discussionmentioning

confidence: 99%

Coronal heating by the partial relaxation of twisted loops

Bareford

Hood

Browning

2013

A&A

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Context. Relaxation theory offers a straightforward method for estimating the energy that is released when continual convective driving causes a magnetic field to become unstable. Thus, an upper limit to the heating caused by ensembles of nanoflaring coronal loops can be calculated and checked against the level of heating required to maintain observed coronal temperatures (T 10 6 K). Aims. We present new results obtained from nonlinear magnetohydrodynamic (MHD) simulations of idealised coronal loops. All of the initial loop configurations discussed are known to be linearly kink unstable. The purpose of this work is to determine whether or not the simulation results agree with Taylor relaxation, which will require a modified version of relaxation theory applicable to unbounded field configurations. In addition, we show for two cases how the relaxation process unfolds. Methods. A three-dimensional (3D) MHD Lagrangian-remap code is used to simulate the evolution of a line-tied cylindrical coronal loop model. This model comprises three concentric layers surrounded by a potential envelope; hence, being twisted locally, each loop configuration is distinguished by a piecewise-constant current profile, featuring three parameters. Initially, all configurations carry zero-net-current fields and are in ideally unstable equilibrium. The simulation results are compared with the predictions of helicityconserving relaxation theory. Results. For all simulations, the change in helicity is no more than 2% of the initial value; also, the numerical helicities match the analytically-determined values. Magnetic energy dissipation predominantly occurs via shock heating associated with magnetic reconnection in distributed current sheets. The energy release and final field profiles produced by the numerical simulations are in agreement with the predictions given by a new model of partial relaxation theory: the relaxed field is close to a linear force free state; however, the extent of the relaxation region is limited, while the loop undergoes some radial expansion. Conclusions. The results presented here support the use of partial relaxation theory, specifically, when calculating the heating-event distributions produced by ensembles of kink-unstable loops. The energy release increases with relaxation radius; but, once the loop has expanded by more than 50%, further expansion yields little more energy. We conclude that the relaxation methodology may be used for coronal heating studies.

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“…Firstly the heating is affected by the amount of energy that can be released in a relaxation on dynamic time-scales. Relaxation preserves the total helicity (Taylor 1974) and possibly also further topological constraints (Yeates et al 2010).…”

Section: Discussionmentioning

confidence: 99%

“…A second feature of the colour map tells us why we cannot relax to a single flux tube in the E 3 simulation (as determined by Yeates et al 2010;Yeates & Hornig 2011). If we walk around the boundary of the domain for E 3 then we meet each of the four colours twice (and in the order red-yellow-green-blue).…”

Section: Topological Propertiesmentioning

confidence: 99%

Heating of braided coronal loops

Wilmot-Smith

Pontin

Yeates

et al. 2011

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Aims. We investigate the relaxation of braided magnetic loops in order to find out how the type of braiding via footpoint motions affects resultant heating of the loop. Methods. Two magnetic loops, braided in different ways, are used as initial conditions in resistive MHD simulations and their subsequent evolution is studied. Results. The fields both undergo a resistive relaxation in which current sheets form and fragment and the system evolves towards a state of lower energy. In one case this relaxation is very efficient with current sheets filling the volume and homogeneous heating of the loop occurring. In the other case fewer current sheets develop, less magnetic energy is released in the process and a patchy heating of the loop results. The two cases, although very similar in their setup, can be distinguished by the mixing properties of the photospheric driver. The mixing can be measured by the topological entropy of the plasma flow, an observable quantity.

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Topological Constraints on Magnetic Relaxation

Cited by 64 publications

References 21 publications

Unique topological characterization of braided magnetic fields

Unique topological characterization of braided magnetic fields

Coronal heating by the partial relaxation of twisted loops

Heating of braided coronal loops

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